The scattering of X-and γ-rays by rings of electrons—A crucial test of the electron ring theory of atoms

Abstract
1. It is generally admitted that the Electron Ring Theory of Atoms, based on the classical electrodynamics and mechanics, does not explain certain results of recent investigations respecting thermal radiation, photoelectric emissions, transformations between corpuscular and X-ray energies and spectrum series. All these phenomena involve the interaction of radiation in one form or another, not merely with electrons, but also with matter, not so much with matter in bulk as with material atoms, and the failure of the Electron Ring Theory to account for them may after all be due rather to our ignorance of atomic structure than to defects in the fundamental principles of the theory itself. Moreover the hypotheses proposed for the explanation of the phenomena in question, such as the Quantum hypothesis, themselves fail to account for other phenomena, such as interference, diffraction and polarisation, which are so familiar to us that the necessity of explaining them afresh is apt to be overlooked when a new theory is introduced. In view of the present unsatisfactory state of our theories and the indecisive character of our experimental knowledge a crucial experimental test of the Electron Ring theory is very much to be desired, especially one involving as little knowledge of atomic structure as possible. The object of the present investigation is to show that the phenomenon of the scattering of X- and γ -rays by matter affords a test of this kind and, moreover, if the issue of the test be favourable, supplies a means of investigating experimentally the arrangement of the electrons in at any rate the lighter atoms. By scattering is meant the redistribution in space without change of frequency of a portion of the radiation incident on matter. For our purpose any radiation of altered frequency, generated by processes akin to fluorescence or phos­phorescence, must be carefully distinguished from scattered radiation. 2. Many years ago Sir J. J. Thomson propounded his well-known theory of the scattering of X- and γ -rays by matter, based mainly on three assumptions: (1) X- and γ -rays consist of extremely thin and intense electro­magnetic pulses; (2) scattering is due entirely to the comparatively mobile electrons of the atom, that due to the relatively inert residue being neglected; and (3) the electromagnetic forces exerted by the pulses on the electrons are so intense that the forces due to other electrons and to the residue of the atom may be left out of account. Two of the results of this theory are important for the purpose of comparison with those of the present investiga­tion: (1) The fraction of the incident energy scattered in a direction making an angle θ with the direction of propagation of the incident beam is proportional to 1 + cos 2 θ ; and (2) the energy scattered every second in all directions together is 8 π e 4 n /3 c 4 m 2 times the intensity of the incident radiation for n electrons all of which scatter effectively, and it is independent of their arrangement. With the usual values, e / c = 1·59 . 10 -20 and e / cm = 1·76 . 10 7 e. m. u ., the coefficient is equal to 0·656 . 10 -24 per electron. If we assume that the hydrogen atom has a mass 1·64 . 10 -24 grm. and contains one mobile electron, we find that the mass scattering coefficient of hydrogen is 0·40. If further we assume that the number of electrons in atoms other than the hydrogen atom is one-half of the atomic weight, we find that the mass scattering coefficients of elements other than hydrogen are all equal to 0·20.

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